Which London site has been the Archbishop of Canterbury's home for over 800 years?

Lambeth Palace is the correct answer because it has served as the official residence of the Archbishop of Canterbury for more than 800 years. The palace, located on the south bank of the River Thames, has been the spiritual and administrative center for the Church of England, housing the archbishops and serving as a place for significant church activities and meetings. Its rich history and continuous use as the residence reflect the long-standing ecclesiastical authority and tradition associated with the position of the Archbishop of Canterbury.

Other locations mentioned have their own historical significance but do not serve the same function. Canterbury Cathedral, while closely associated with the Archbishop, is primarily a place of worship and pilgrimage rather than a residence. Westminster Abbey is renowned as a site for royal ceremonies, such as coronations, and is not specifically tied to the Archbishop's living arrangements. The Tower of London, known for its history as a royal fortress and prison, also does not pertain to the residence of the Archbishop of Canterbury. Thus, Lambeth Palace stands out as the enduring home for this high church authority.